This observation indicates the pressure switch is working fine. If it were not you would never have gas flowing.

"Disconnecting the connector to the pressure switch and checking the voltage at the connector it remains at a steady 24VAC"

Does the above happen with the gas flowing too?

I would double check your AC voltage measurements. If you look on the control board you should find a small relay that's used to power the HSI. Possibly that relay is the problem. Check the board for any signs of loose connections/cold solder joints. You can always jumper the pressure switch connector to totally remove the switch from the circuit but I doubt it's the switch... they work or they don't.

Another possibility is the gas valve solenoid, when activated opening the gas valve, is causing the voltage drop. You can measure the impedance of the solenoid coil and see if it's correct. Also check the transformer connections to the control board.

That Siemens device may be the relay. There should be 2 traces to the coil side (24 volts) and 2 leads on the switch side (120 volts) going to the HSI. Check the traces on the 120 volt side for cold solder joints/loose connection. Check the socket and connector. Check for 120 volts on the load side of the relay.

Find where the 24 volt AC transformer is located and while calling for heat measure the voltage on the 24 volt side of the transformer making sure it stays constant at around 24 volts AC. We'll work our way to the HSI making sure we don't miss the real problem by jumping ahead. But since you originally said the gas flows but doesn't ignite, due to the HSI malfunctioning, it does seem the HSI circuit is the problem.

If you can be sure it is a relay problem and can find it online, replacing it is easy if you're handy with a soldering iron.